7.2.1 Linear Inequalities, PT3 Focus Practice - Mathematics

7.2.1 Linear Inequalities, PT3 Focus Practice

Question 1:

Draw a number line to represent the solution for the linear inequalities –3 < 5 – x ≤ 4.

Solution:

–3 < 5 – x and 5 – x ≤ 4

x < 5 + 3 and –x ≤ 4 – 5

x < 8 and –x ≤ –1 → x ≥ 1

Thus, the solution is 1 ≤ x < 8

Question 2:

Solve the following simultaneous linear inequalities.

3 x - 5 \leq 1 and 2 - \frac{1}{3} x < 3

Solution:

3x – 5 ≤ 1

3x ≤ 1 + 5

3x ≤ 6

x ≤ 2

\begin{array}{l} 2 - \frac{1}{3} x < 3 \\ 6 - x < 9 \leftarrow Multiply by 3 \\ - x < 9 - 6 \\ - x < 3 \\ x > - 3 \leftarrow Multiply by - 1 \end{array}

The solution is –3 < x ≤ 2.

Question 3:

The solution for the inequality 2 + x < 3x – 4 is

Solution:

2 + x < 3x – 4

x – 3x < –4 – 2

–2x < –6

–x < –3

x > 3

Question 4:

The solution for the inequality –2 (6y + 3) < 3 (4 – 2y) is

Solution:

–2 (6y + 3) < 3 (4 – 2y)

–12y – 6 < 12 – 6y

–12y + 6y < 12 + 6

–6y < 18

–y < 3

y > –3